The return of Beelzenef

Ok, Beelzenef is completed!


First we have prototype-Beelzenef! This was knitting in the round, all in one piece on dpns. I haven't used them for a while, but I'm loving dpns just now. Niftily, he has almost no seams.



Then we have the final Beelzenef. This one is much bigger, and made with thicker wool He was knitting flat to allow me to use intarsia for the eyes and mouth. I'm not entirely happy with how the eyes turned out - I intarsed white patches and sewed on black outlines afterwards, but because the intarsia patches are quite blocky the two don't exactly match up, which I think makes it look a little scruffy. Hopefully that only shows if you're looking closely.
Another problem is that he doesn't quite bend like the prototype, so it was difficult to gesture with him. I suspect the (accidentally) untwisted make stitches on the prototype helped with this, giving it more of a crease to fold along. Possibly the thicker wool contributed to this too. Or perhaps the arms need to be placed more at the front? I guess I'll need to experiment more, which is good, because I had a lot of fun making these :).



In the meantime, here's Beelzenef as part of the full Nekozawa costume:

Alexander horned sphere

More maths geeking for this project, and a return(sort of) of the tori!

In two dimensions, the Jordan-Schonflies curve theorem says that if you have a shape in the plane which is topologically equivalent to a circle, then there is a homeomorphism(topological equivalence) of the place making this into the standard circle in the plane. In higher dimensions this isn't true, and to my mind this is one of the big differences between 2D and higher dimensions.
The Alexander horned sphere is the standard counterexample to this. To construct it, you take a sphere, then you pick two discs on it, and stretch them into a kind of claw. Then you pick two discs on the end of each 'horn' and form another claw, with the two claws interlocking but never touching. You can do this infinitely many times, and you need to add in a few points(actually these points form a kind of Cantor set. I'm not quite clear on how this step works) to get a complete sphere. This picture probably makes the construction clearer.
Then if you imagine passing a loop through the middle of this thing and trying to take it out, you find it's impossible - you need to bend it through infinitely many horns or ever smaller size, and topology won't let you. This can never happen with the standard sphere - any loop on the outside can be pulled down to a point, so the 'outside' of this sphere is very different from the outside of the standard one.
Because it has this hole in the middle, I like to think of this as a kind of honourary torus.

In theory, the knitting of this is made easier by self-similarity - each of the smaller horns should be a scaled down version of the big of the big one, so you should be able to write a pattern for the big one, then the smaller ones are all multiples of this. Unfortunately I can't figure out quite how the horns need to be arranged to make this work - the crucial question is what angle they need to make with each other for this to happen. So to get around this, I'm planning to just knit it one layer at a time - I'll make the big piece first, then I'll be able to measure and find out how big the next level of horns should be. It's a little less satisfying than working it out directly, but maybe once I've made this I'll be able to get my head around how it's arranged enough to work it out explicitly.
I'm planning to knit the first three levels of horns, each in different colours to highlight some of the hierarchy, then represent the fourth level with sewn stitches which will hold the thing together.

I'm also toying with the idea that at some point in the future this could be used as part of an Alexander horned deer, because the sheer horror on people's faces when I explain that pun would be worth the effort alone.

Hugh.

Cthulhu mittens

More evil knitting! I came across this Lord of the Rings hoodie a while back and thought it was very cool, but I'm not hugely keen on LotR. I am, on the other hand, quite keen on HP Lovecraft, who was also very keen on runes, and thus began the Cthulhu mittens scheme.
As far as I know, Lovecraft never illustrated any of the runes, but there is a roleplaying game of the Cthulhu mythos which does, named The Call of Cthulhu.

The plan is to have a ring of small runes around the cuff, and a single large sign in the middle. I decided to kind of fudge this - the cuff is knit in the round, so it's all one piece, then the front and back are knit seperately as two flat pieces and sewn together so that the big rune can be intarsia-d.

Beelzenef

Ok, next geeky project - to knit the glove puppet Beelzenef from Ouran High. Yay anime geekery!

Ouran High School Host Club is an anime comedy series about a... slightly eccentric high school for the (slightly eccentric) children of rich and famous families. One of it's members is Nekozawa, the son of a family with a dark and mysterious past, who is president of the school's black magic society. He carries with him, at all times, a cat glove puppet named Beelzenef, who may be some kind of a familiar, and may be a family heirloom(I'm a little shaky on the detail).
So, always keen to knit evil or sinister things, I was wanting to try knitting a Beelzenef, and when a friend mentioned he was considering cosplaying as Nekozawa at a nearby anime convention, I volunteered this as part of his costume.

Knitting-wise, this will be largely a modified mitten, with a thumb on each side to function as arms, and two cones added at the top as ears. For the final version I'll intarsia the eyes and mouth.

Hugh.

Surface of genus three

This is going to be a birthday present for my (maths geek) older brother. The surface of genus 3 is made of three tori stuck together. Alternatively, you can take a sphere and stick three handles onto it.
There's a theorem in geometry(the Poincare-Hopf theorem) which tells you what kind of vector fields you can put onto different shapes, and particularly about the kind of zeroes they have to have. One consequence of this is that only very specific shapes can be combed without leaving any bald spots or tufts, and the surface of genus 3 is not one of these(in fact the torus is the only compact orientable surface for which this is possible).
So the plan is to make this surface out of combable wool, so you can physically demonstrate this.
Niftily, there's a similar result which says the odd dimensional, but not the even ones, can be combed, is (sometimes) known as 'hedgehog combing'.




Knitting-wise, I'll make this in three pieces, each one consisting of a torus with a strip cut out, and a small tube sticking out to attach them together. This probably isn't the best way to do this, but I'm quite squeamish about doing anything too complicated with fluffy wool.

Sorry about the rubbish pictures, I haven't found a good drawing program for my diagrams yet.

Hugh.

Shiny new blogging

Hi people!
I've been persuaded to start a blog collecting together my various geeky
knitting projects. My hope is this will give people a chance to see the
finished articles, allow me to explain some of the geek-background
involved, and maybe give people some ideas for projects of their own.

So come on in, hope you like it :o)
Man-with-pointy-sticks Hugh.